List of top Mathematics Questions

The value of $\sin 18^{\circ}$ is

The equation of the tangent to the curve $y = 4x e^x$ at $\left(-1, -\frac{4}{e}\right)$ is

If $\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$, then $f(x)=$

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is

The domain of the function $f(x) = \frac{1}{\sqrt{x + |x|}}$ is

The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio

The angle between a line with direction ratios 2, 2, 1 and a line joining $(3, 1, 4)$ and $(7, 2, 12)$ is

The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is

$(2\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 27\hat{\mathrm{k}}) \times (\hat{\mathrm{i}} + \lambda\hat{\mathrm{j}} + \mu\hat{\mathrm{k}}) = \vec{0}$, then $\lambda$ and $\mu$ are respectively

If $f(x) = [x]$, for $x \in (-1, 2)$, then $f$ is discontinuous at (where $[x]$ represents floor function)

If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are cofactors of the elements $a_{ij}$ of $A$, then $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$ is equal to

The general solution of the differential equation $x + y \frac{d y}{d x} = \sec(x^2 + y^2)$ is

The value of $(1 + i)^5 (1 - i)^7$ is

The area of the region bounded by the parabola $x^2 = y$ and the line $y = x$ is

$\lim_{x \to \infty} \left( \sqrt{x^2 + 5x - 7} - x \right) =$

Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000 for the next five years. Considering the experience of VCR users, the following distribution of maintenance expenses for the next five years is formed.

The expected value of maintenance cost is :

If inverse of $\begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix}$ does not exist, then $x =$

The general solution of the differential equation $\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$ is given by

The logical expression $p \wedge(\sim p \vee \sim q) \equiv$

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of $k$ is

The parametric equations of a line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$ are

A particle is moving on a straight line. The distance S travelled in time t is given by $S = a t^2 + b t + 6$. If the particle comes to rest after 4 seconds at a distance of 16 m from the starting point, then the acceleration of the particle is

If $y=\log \tan \left(\frac{x}{2}\right)+\sin ^{-1}(\cos x)$, then $\frac{d y}{d x}=$

The Cartesian equation of the plane passing through the point $(0,7,-7)$ and containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ is